library(knn.covertree)
library(pbapply)
library(ggplot2)
dropout_percent <- c(0,5,10,20,30,40,50,75,80,85,90,95)
counts_path <- sapply(dropout_percent, function(y) paste0("/Users/elise/Desktop/GitHub/Hubness_sc/bulkRNAseq/simul",y,".csv"))
pca_path <- sapply(dropout_percent, function(y) paste0("/Users/elise/Desktop/GitHub/Hubness_sc/bulkRNAseq/simul_pca_readyforhubness",y,".csv"))
sdev_path <- sapply(dropout_percent, function(y) paste0("/Users/elise/Desktop/GitHub/Hubness_sc/bulkRNAseq/simul_pca_sdev",y,".csv"))
simul <- pblapply(counts_path, function(x) read.table(x))
simul_pca <- pblapply(pca_path, function(x) read.table(x))
sdev<-pblapply(sdev_path, function(x) read.table(file=x))
sdev <- pblapply(sdev, function(x) return(x/x[1,1]))
source(file="/Users/elise/Desktop/GitHub/Hubness_sc/R_scripts/load_data/hubness_load_write_data_simul.R")
hubness <- lapply(hubness, function(x) {x$cellID <- names(hubness_scores_data[[1]][[1]][[1]]); return(x)})
get_hub_scores <- function(data,k) {
  knn_graph <- knn.covertree::find_knn(t(data),k)
  knn_list <- knn_graph$index
  occurence <- pbsapply(1:nrow(knn_list), function(x) {sum(knn_list==x)})
  return(occurence)
}
asymmetry_evaluation <- function(data) {
  knn_graph <- knn.covertree::find_knn(t(data),k)
  knn_list <- knn_graph$index
  increment = 0
  for (i in 1:nrow(knn_list)) {
    for (j in 1:ncol(knn_list)) {
      if (i %in% knn_list[knn_list[i,j],]) {
        increment <- increment + 1 
      }
    }
  }
  return(1-increment/(nrow(knn_list)*ncol(knn_list)))
}
skewness <- function(distrib) {
  return(mean((distrib-mean(distrib))^3)/(sd(distrib)^3))
}
antihub <- function(distrib) {
  return(sum(distrib==0))
}
k_thd <- function(distrib,k) {
  return(sum(distrib>=2*k))
} 
meansd_thd <- function(distrib) {
  thd <- mean(distrib) + 3*sd(distrib)
  return(sum(distrib>=thd))
}
generate_gaussian <- function(n,dim) {
  return(t(sapply(1:dim, function(x) rnorm(n))))
}
generate_uniform <- function(n,dim) {
  return(t(sapply(1:dim, function(x) runif(n,min=(-1)))))
}
relative_contrast <- function(data) {
  tmp <- as.matrix(dist(t(data)))
  diag(tmp) <- NA
  rc <- apply(tmp, 1, function(x) abs(max(x, na.rm = T)-min(x, na.rm = T))/min(x, na.rm = T))
  return(mean(rc))
}
k=50
dim_val=unique(hubness[[1]]$Dimension)
scores <- pblapply(hubness, function(x) {tmp <- x[x$p==2 & x$k==k,]; score<-pblapply(dim_val, function(y) return(tmp$score[tmp$Dimension==y])); return(score)})
lapply(scores, function(x) lapply(x, hist))

## [[1]]
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## [11] 1.648805e-05 1.648805e-05 1.648805e-05
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## $mids
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## 
## $xname
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## $equidist
## [1] TRUE
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## [[1]][[8]]
## $breaks
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## $counts
##  [1] 1079   57   23   19   11    6    5    5    6    0    1    1
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## $density
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##  [6] 4.946414e-05 4.122012e-05 4.122012e-05 4.946414e-05 0.000000e+00
## [11] 8.244023e-06 8.244023e-06
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## $mids
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## 
## $xname
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## attr(,"class")
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## [[1]][[9]]
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## $counts
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##  [6] 2.473207e-05 2.473207e-05 4.122012e-05 4.122012e-05 7.419621e-05
## [11] 4.946414e-05 1.401484e-04 2.473207e-05
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## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
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## $equidist
## [1] TRUE
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## attr(,"class")
## [1] "histogram"
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## [[1]][[10]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300
## 
## $counts
##  [1] 1145    6    3    3    5    2    1    1    5    3    7   13   19
## 
## $density
##  [1] 9.439406e-03 4.946414e-05 2.473207e-05 2.473207e-05 4.122012e-05
##  [6] 1.648805e-05 8.244023e-06 8.244023e-06 4.122012e-05 2.473207e-05
## [11] 5.770816e-05 1.071723e-04 1.566364e-04
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
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## [[1]][[11]]
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## 
## $counts
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## 
## $density
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## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
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## $xname
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## $equidist
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## attr(,"class")
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## 
## [[2]]
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## $breaks
##  [1]  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
## 
## $counts
##  [1]  10  11  16  26  34  54  65 108 244 239 170 140  68  26   2
## 
## $density
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## $xname
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## $equidist
## [1] TRUE
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## attr(,"class")
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## [[2]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
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## $counts
##  [1]  15  70 163 170 183 207 193 138  64  10
## 
## $density
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## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
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## $xname
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## $equidist
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## attr(,"class")
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## [[2]][[3]]
## $breaks
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## $density
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## $mids
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## $equidist
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## [[2]][[4]]
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## $counts
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## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
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## attr(,"class")
## [1] "histogram"
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## [[2]][[5]]
## $breaks
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## $counts
##  [1] 300 347 215 132  79  48  42  18  10   7   8   2   3   1   0   0   1
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## $density
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## [16] 0.000000e+00 4.122012e-05
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## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290 310 330
## 
## $xname
## [1] "X[[i]]"
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## [1] TRUE
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## [[2]][[6]]
## $breaks
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## $counts
##  [1] 801 269  83  36  15   3   4   1   0   1
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##  [6] 4.946414e-05 6.595218e-05 1.648805e-05 0.000000e+00 1.648805e-05
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## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
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## $xname
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## $equidist
## [1] TRUE
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## [[2]][[7]]
## $breaks
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## $counts
##  [1] 802 248 103  28  19   7   3   1   1   0   1
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## $density
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##  [6] 1.154163e-04 4.946414e-05 1.648805e-05 1.648805e-05 0.000000e+00
## [11] 1.648805e-05
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## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
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## [[2]][[8]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100
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## $counts
##  [1] 1039  113   35   16    4    4    1    0    0    0    1
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## $density
##  [1] 8.565540e-03 9.315746e-04 2.885408e-04 1.319044e-04 3.297609e-05
##  [6] 3.297609e-05 8.244023e-06 0.000000e+00 0.000000e+00 0.000000e+00
## [11] 8.244023e-06
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
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## [[2]][[9]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300
## 
## $counts
##  [1] 1102   28   13   14   11    6    9    4    5    5    2    6    8
## 
## $density
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##  [6] 4.946414e-05 7.419621e-05 3.297609e-05 4.122012e-05 4.122012e-05
## [11] 1.648805e-05 4.946414e-05 6.595218e-05
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
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## [[2]][[10]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300
## 
## $counts
##  [1] 1127   13   11   11    2    4    7    5    3    1    7   11   11
## 
## $density
##  [1] 9.291014e-03 1.071723e-04 9.068425e-05 9.068425e-05 1.648805e-05
##  [6] 3.297609e-05 5.770816e-05 4.122012e-05 2.473207e-05 8.244023e-06
## [11] 5.770816e-05 9.068425e-05 9.068425e-05
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## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
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## [[2]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200
## 
## $counts
##  [1] 1113    3    6    8   13   19   18   15    8    6    3    1
## 
## $density
##  [1] 9.175598e-03 2.473207e-05 4.946414e-05 6.595218e-05 1.071723e-04
##  [6] 1.566364e-04 1.483924e-04 1.236603e-04 6.595218e-05 4.946414e-05
## [11] 2.473207e-05 8.244023e-06
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## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150
## 
## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
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## [[3]]
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## $breaks
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## 
## $counts
##  [1]   1   5  13  22  30  39  60  91 124 157 183 223 159  68  36   1   1
## 
## $density
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##  [6] 0.0064303380 0.0098928277 0.0150041220 0.0204451772 0.0258862325
## [11] 0.0301731245 0.0367683430 0.0262159934 0.0112118714 0.0059356966
## [16] 0.0001648805 0.0001648805
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
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## $xname
## [1] "X[[i]]"
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## $equidist
## [1] TRUE
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## attr(,"class")
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## [[3]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100 110
## 
## $counts
##  [1]  20  75 144 175 180 206 205 144  53  10   1
## 
## $density
##  [1] 1.648805e-03 6.183017e-03 1.187139e-02 1.442704e-02 1.483924e-02
##  [6] 1.698269e-02 1.690025e-02 1.187139e-02 4.369332e-03 8.244023e-04
## [11] 8.244023e-05
## 
## $mids
##  [1]   5  15  25  35  45  55  65  75  85  95 105
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[3]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100 110 120 130 140 150 160 170
## 
## $counts
##  [1]  44 118 139 207 180 165 106  86  69  31  27  17   6  15   1   1   1
## 
## $density
##  [1] 3.627370e-03 9.727947e-03 1.145919e-02 1.706513e-02 1.483924e-02
##  [6] 1.360264e-02 8.738664e-03 7.089860e-03 5.688376e-03 2.555647e-03
## [11] 2.225886e-03 1.401484e-03 4.946414e-04 1.236603e-03 8.244023e-05
## [16] 8.244023e-05 8.244023e-05
## 
## $mids
##  [1]   5  15  25  35  45  55  65  75  85  95 105 115 125 135 145 155 165
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[4]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280 300 320
## 
## $counts
##  [1] 263 361 237 142  97  45  24  24  11   1   2   3   0   1   1   1
## 
## $density
##  [1] 1.084089e-02 1.488046e-02 9.769167e-03 5.853256e-03 3.998351e-03
##  [6] 1.854905e-03 9.892828e-04 9.892828e-04 4.534213e-04 4.122012e-05
## [11] 8.244023e-05 1.236603e-04 0.000000e+00 4.122012e-05 4.122012e-05
## [16] 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290 310
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 760 327  78  33   8   4   1   1   1
## 
## $density
## [1] 1.253092e-02 5.391591e-03 1.286068e-03 5.441055e-04 1.319044e-04
## [6] 6.595218e-05 1.648805e-05 1.648805e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 805 251  95  34  19   6   2   0   1
## 
## $density
## [1] 1.327288e-02 4.138500e-03 1.566364e-03 5.605936e-04 3.132729e-04
## [6] 9.892828e-05 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 816 236  80  46  25   5   2   2   1
## 
## $density
## [1] 1.345425e-02 3.891179e-03 1.319044e-03 7.584501e-04 4.122012e-04
## [6] 8.244023e-05 3.297609e-05 3.297609e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 862 173  77  43  19  14   7   7   5   1   3   0   2
## 
## $density
##  [1] 1.421270e-02 2.852432e-03 1.269580e-03 7.089860e-04 3.132729e-04
##  [6] 2.308326e-04 1.154163e-04 1.154163e-04 8.244023e-05 1.648805e-05
## [11] 4.946414e-05 0.000000e+00 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[9]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300
## 
## $counts
##  [1] 1096   31   16   18    8    6   14    6    4    2    3    5    4
## 
## $density
##  [1] 9.035449e-03 2.555647e-04 1.319044e-04 1.483924e-04 6.595218e-05
##  [6] 4.946414e-05 1.154163e-04 4.946414e-05 3.297609e-05 1.648805e-05
## [11] 2.473207e-05 4.122012e-05 3.297609e-05
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[10]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300
## 
## $counts
##  [1] 1105   32   15   10    6    5    3    8    6    7    2    9    5
## 
## $density
##  [1] 9.109646e-03 2.638087e-04 1.236603e-04 8.244023e-05 4.946414e-05
##  [6] 4.122012e-05 2.473207e-05 6.595218e-05 4.946414e-05 5.770816e-05
## [11] 1.648805e-05 7.419621e-05 4.122012e-05
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050 1150 1250
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[3]][[11]]
## $breaks
##  [1]   0 100 200 300 400 500 600 700 800 900
## 
## $counts
## [1] 1113    0    0    7   21   22   18   23    9
## 
## $density
## [1] 9.175598e-03 0.000000e+00 0.000000e+00 5.770816e-05 1.731245e-04
## [6] 1.813685e-04 1.483924e-04 1.896125e-04 7.419621e-05
## 
## $mids
## [1]  50 150 250 350 450 550 650 750 850
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[4]]
## [[4]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   1   6   9  35  41  56  60  92  98 129 183 194 174  85  37   9   4
## 
## $density
##  [1] 0.0001648805 0.0009892828 0.0014839242 0.0057708162 0.0067600989
##  [6] 0.0092333059 0.0098928277 0.0151690025 0.0161582852 0.0212695796
## [11] 0.0301731245 0.0319868096 0.0286892003 0.0140148392 0.0061005771
## [16] 0.0014839242 0.0006595218
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
## 
## $counts
##  [1]  16  82 140 192 167 219 176 147  65   9
## 
## $density
##  [1] 0.0013190437 0.0067600989 0.0115416323 0.0158285243 0.0137675185
##  [6] 0.0180544106 0.0145094806 0.0121187139 0.0053586150 0.0007419621
## 
## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[3]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100 110 120 130 140 150 160 170
## 
## $counts
##  [1]  50 126 167 194 170 127  99 102  62  39  29  21  10   5   8   2   2
## 
## $density
##  [1] 0.0041220115 0.0103874691 0.0137675185 0.0159934048 0.0140148392
##  [6] 0.0104699093 0.0081615829 0.0084089035 0.0051112943 0.0032151690
## [11] 0.0023907667 0.0017312448 0.0008244023 0.0004122012 0.0006595218
## [16] 0.0001648805 0.0001648805
## 
## $mids
##  [1]   5  15  25  35  45  55  65  75  85  95 105 115 125 135 145 155 165
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[4]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280
## 
## $counts
##  [1] 315 337 215 148  70  35  31  19  11  10   9   6   4   3
## 
## $density
##  [1] 0.0129843364 0.0138911789 0.0088623248 0.0061005771 0.0028854081
##  [6] 0.0014427040 0.0012778236 0.0007831822 0.0004534213 0.0004122012
## [11] 0.0003709810 0.0002473207 0.0001648805 0.0001236603
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 788 283  94  21  10   8   6   2   0   1
## 
## $density
##  [1] 1.299258e-02 4.666117e-03 1.549876e-03 3.462490e-04 1.648805e-04
##  [6] 1.319044e-04 9.892828e-05 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 794 260 100  32  15   3   5   3   1
## 
## $density
## [1] 1.309151e-02 4.286892e-03 1.648805e-03 5.276175e-04 2.473207e-04
## [6] 4.946414e-05 8.244023e-05 4.946414e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 830 234  71  36  24   7   7   2   0   1   1
## 
## $density
##  [1] 1.368508e-02 3.858203e-03 1.170651e-03 5.935697e-04 3.957131e-04
##  [6] 1.154163e-04 1.154163e-04 3.297609e-05 0.000000e+00 1.648805e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 830 206  88  42  24   9   6   2   4   1   0   0   1
## 
## $density
##  [1] 1.368508e-02 3.396538e-03 1.450948e-03 6.924979e-04 3.957131e-04
##  [6] 1.483924e-04 9.892828e-05 3.297609e-05 6.595218e-05 1.648805e-05
## [11] 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[9]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1058   62   38   26   11    2    7    6    1    2
## 
## $density
##  [1] 8.722176e-03 5.111294e-04 3.132729e-04 2.143446e-04 9.068425e-05
##  [6] 1.648805e-05 5.770816e-05 4.946414e-05 8.244023e-06 1.648805e-05
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[10]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100
## 
## $counts
##  [1] 1069   65   22   12   11   12    4   10    3    3    2
## 
## $density
##  [1] 8.812861e-03 5.358615e-04 1.813685e-04 9.892828e-05 9.068425e-05
##  [6] 9.892828e-05 3.297609e-05 8.244023e-05 2.473207e-05 2.473207e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[4]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1113    0    1    4   16   28   26   19    5    1
## 
## $density
##  [1] 9.175598e-03 0.000000e+00 8.244023e-06 3.297609e-05 1.319044e-04
##  [6] 2.308326e-04 2.143446e-04 1.566364e-04 4.122012e-05 8.244023e-06
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[5]]
## [[5]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   1   7  14  27  33  59  74  94 107 139 151 177 163 103  46  16   2
## 
## $density
##  [1] 0.0001648805 0.0011541632 0.0023083265 0.0044517725 0.0054410552
##  [6] 0.0097279472 0.0122011542 0.0154987634 0.0176422094 0.0229183842
## [11] 0.0248969497 0.0291838417 0.0268755153 0.0169826876 0.0075845012
## [16] 0.0026380874 0.0003297609
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100 110
## 
## $counts
##  [1]  17  75 134 190 202 201 174 143  66  10   1
## 
## $density
##  [1] 1.401484e-03 6.183017e-03 1.104699e-02 1.566364e-02 1.665293e-02
##  [6] 1.657049e-02 1.434460e-02 1.178895e-02 5.441055e-03 8.244023e-04
## [11] 8.244023e-05
## 
## $mids
##  [1]   5  15  25  35  45  55  65  75  85  95 105
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200
## 
## $counts
##  [1] 206 332 289 205  92  57  22   8   1   1
## 
## $density
##  [1] 8.491344e-03 1.368508e-02 1.191261e-02 8.450124e-03 3.792251e-03
##  [6] 2.349547e-03 9.068425e-04 3.297609e-04 4.122012e-05 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[4]]
## $breaks
## [1]   0  50 100 150 200 250 300 350 400
## 
## $counts
## [1] 784 289  92  30  10   4   3   1
## 
## $density
## [1] 1.292663e-02 4.765045e-03 1.516900e-03 4.946414e-04 1.648805e-04
## [6] 6.595218e-05 4.946414e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 796 267  86  32  17  12   1   1   1
## 
## $density
## [1] 1.312448e-02 4.402308e-03 1.417972e-03 5.276175e-04 2.802968e-04
## [6] 1.978566e-04 1.648805e-05 1.648805e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 803 250  97  35  17   8   2   0   1
## 
## $density
## [1] 1.323990e-02 4.122012e-03 1.599340e-03 5.770816e-04 2.802968e-04
## [6] 1.319044e-04 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 808 241  97  40  17   5   4   0   1
## 
## $density
## [1] 1.332234e-02 3.973619e-03 1.599340e-03 6.595218e-04 2.802968e-04
## [6] 8.244023e-05 6.595218e-05 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 808 229 105  36  21   6   3   1   2   1   0   0   1
## 
## $density
##  [1] 1.332234e-02 3.775763e-03 1.731245e-03 5.935697e-04 3.462490e-04
##  [6] 9.892828e-05 4.946414e-05 1.648805e-05 3.297609e-05 1.648805e-05
## [11] 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[9]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650 700 750
## 
## $counts
##  [1] 888 158  56  35  36  12  12   2   5   2   3   1   1   0   2
## 
## $density
##  [1] 1.464138e-02 2.605111e-03 9.233306e-04 5.770816e-04 5.935697e-04
##  [6] 1.978566e-04 1.978566e-04 3.297609e-05 8.244023e-05 3.297609e-05
## [11] 4.946414e-05 1.648805e-05 1.648805e-05 0.000000e+00 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625 675 725
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
## 
## $counts
##  [1] 885 147  74  38  19  17  10   9   3   2   3   1   1   2   1   1
## 
## $density
##  [1] 1.459192e-02 2.423743e-03 1.220115e-03 6.265458e-04 3.132729e-04
##  [6] 2.802968e-04 1.648805e-04 1.483924e-04 4.946414e-05 3.297609e-05
## [11] 4.946414e-05 1.648805e-05 1.648805e-05 3.297609e-05 1.648805e-05
## [16] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625 675 725 775
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[5]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1113    0    1    5   17   26   25   19    6    1
## 
## $density
##  [1] 9.175598e-03 0.000000e+00 8.244023e-06 4.122012e-05 1.401484e-04
##  [6] 2.143446e-04 2.061006e-04 1.566364e-04 4.946414e-05 8.244023e-06
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[6]]
## [[6]][[1]]
## $breaks
##  [1]  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   5  21  32  40  61  90  86 107 110 143 145 171 122  64  13   3
## 
## $density
##  [1] 0.0008244023 0.0034624897 0.0052761748 0.0065952185 0.0100577082
##  [6] 0.0148392415 0.0141797197 0.0176422094 0.0181368508 0.0235779060
## [11] 0.0239076669 0.0281945589 0.0201154163 0.0105523495 0.0021434460
## [16] 0.0004946414
## 
## $mids
##  [1]  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5 77.5
## [16] 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
## 
## $counts
##  [1]  23  76 140 167 203 207 172 150  68   7
## 
## $density
##  [1] 0.0018961253 0.0062654575 0.0115416323 0.0137675185 0.0167353669
##  [6] 0.0170651278 0.0141797197 0.0123660346 0.0056059357 0.0005770816
## 
## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180
## 
## $counts
## [1] 226 331 271 183  95  54  40  10   3
## 
## $density
## [1] 0.0093157461 0.0136438582 0.0111706513 0.0075432811 0.0039159110
## [6] 0.0022258862 0.0016488046 0.0004122012 0.0001236603
## 
## $mids
## [1]  10  30  50  70  90 110 130 150 170
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[4]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 801 266  91  34  14   4   2   0   1
## 
## $density
## [1] 1.320692e-02 4.385820e-03 1.500412e-03 5.605936e-04 2.308326e-04
## [6] 6.595218e-05 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 801 260  80  44  19   5   0   3   0   1
## 
## $density
##  [1] 1.320692e-02 4.286892e-03 1.319044e-03 7.254740e-04 3.132729e-04
##  [6] 8.244023e-05 0.000000e+00 4.946414e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 816 233  90  42  16   9   2   2   2   0   1
## 
## $density
##  [1] 1.345425e-02 3.841715e-03 1.483924e-03 6.924979e-04 2.638087e-04
##  [6] 1.483924e-04 3.297609e-05 3.297609e-05 3.297609e-05 0.000000e+00
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 801 253  87  39  16   7   6   1   3
## 
## $density
## [1] 1.320692e-02 4.171476e-03 1.434460e-03 6.430338e-04 2.638087e-04
## [6] 1.154163e-04 9.892828e-05 1.648805e-05 4.946414e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 819 223  98  37  15  11   5   3   1   0   1
## 
## $density
##  [1] 1.350371e-02 3.676834e-03 1.615829e-03 6.100577e-04 2.473207e-04
##  [6] 1.813685e-04 8.244023e-05 4.946414e-05 1.648805e-05 0.000000e+00
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[9]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 818 242  79  34  16   8   9   3   2   1   1
## 
## $density
##  [1] 1.348722e-02 3.990107e-03 1.302556e-03 5.605936e-04 2.638087e-04
##  [6] 1.319044e-04 1.483924e-04 4.946414e-05 3.297609e-05 1.648805e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 862 159  85  37  34  12  12   4   3   4   1
## 
## $density
##  [1] 1.421270e-02 2.621599e-03 1.401484e-03 6.100577e-04 5.605936e-04
##  [6] 1.978566e-04 1.978566e-04 6.595218e-05 4.946414e-05 6.595218e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[6]][[11]]
## $breaks
##  [1]   0 100 200 300 400 500 600 700 800 900
## 
## $counts
## [1] 1113    0    0    6   15   26   29   17    7
## 
## $density
## [1] 9.175598e-03 0.000000e+00 0.000000e+00 4.946414e-05 1.236603e-04
## [6] 2.143446e-04 2.390767e-04 1.401484e-04 5.770816e-05
## 
## $mids
## [1]  50 150 250 350 450 550 650 750 850
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[7]]
## [[7]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
## 
## $counts
##  [1]   1  10  19  26  51  62  65  89 103 120 128 177 179 107  65  11
## 
## $density
##  [1] 0.0001648805 0.0016488046 0.0031327288 0.0042868920 0.0084089035
##  [6] 0.0102225886 0.0107172300 0.0146743611 0.0169826876 0.0197856554
## [11] 0.0211046991 0.0291838417 0.0295136026 0.0176422094 0.0107172300
## [16] 0.0018136851
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
## 
## $counts
##  [1]  28  63 146 185 169 210 197 152  56   7
## 
## $density
##  [1] 0.0023083265 0.0051937345 0.0120362737 0.0152514427 0.0139323990
##  [6] 0.0173124485 0.0162407255 0.0125309151 0.0046166529 0.0005770816
## 
## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200
## 
## $counts
##  [1] 236 351 269 145  98  53  32  19   9   1
## 
## $density
##  [1] 9.727947e-03 1.446826e-02 1.108821e-02 5.976917e-03 4.039571e-03
##  [6] 2.184666e-03 1.319044e-03 7.831822e-04 3.709810e-04 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[4]]
## $breaks
## [1]   0  50 100 150 200 250 300 350 400
## 
## $counts
## [1] 788 279  96  20  19   6   4   1
## 
## $density
## [1] 1.299258e-02 4.600165e-03 1.582852e-03 3.297609e-04 3.132729e-04
## [6] 9.892828e-05 6.595218e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600
## 
## $counts
##  [1] 824 233  94  26  16  10   6   1   1   0   1   1
## 
## $density
##  [1] 1.358615e-02 3.841715e-03 1.549876e-03 4.286892e-04 2.638087e-04
##  [6] 1.648805e-04 9.892828e-05 1.648805e-05 1.648805e-05 0.000000e+00
## [11] 1.648805e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 812 241  88  34  19   8   7   1   1   1   0   0   1
## 
## $density
##  [1] 1.338829e-02 3.973619e-03 1.450948e-03 5.605936e-04 3.132729e-04
##  [6] 1.319044e-04 1.154163e-04 1.648805e-05 1.648805e-05 1.648805e-05
## [11] 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 820 233  86  43  12   9   4   3   0   2   1
## 
## $density
##  [1] 1.352020e-02 3.841715e-03 1.417972e-03 7.089860e-04 1.978566e-04
##  [6] 1.483924e-04 6.595218e-05 4.946414e-05 0.000000e+00 3.297609e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 837 208  88  39  20   8   7   3   1   1   0   0   1
## 
## $density
##  [1] 1.380049e-02 3.429514e-03 1.450948e-03 6.430338e-04 3.297609e-04
##  [6] 1.319044e-04 1.154163e-04 4.946414e-05 1.648805e-05 1.648805e-05
## [11] 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[9]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 799 271  80  37  16   5   2   2   0   1
## 
## $density
##  [1] 1.317395e-02 4.468261e-03 1.319044e-03 6.100577e-04 2.638087e-04
##  [6] 8.244023e-05 3.297609e-05 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650 700
## 
## $counts
##  [1] 872 164  71  44  29   9   4  10   3   2   3   1   0   1
## 
## $density
##  [1] 1.437758e-02 2.704040e-03 1.170651e-03 7.254740e-04 4.781533e-04
##  [6] 1.483924e-04 6.595218e-05 1.648805e-04 4.946414e-05 3.297609e-05
## [11] 4.946414e-05 1.648805e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625 675
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[7]][[11]]
## $breaks
##  [1]   0 100 200 300 400 500 600 700 800 900
## 
## $counts
## [1] 1113    0    0   10   20   18   21   20   11
## 
## $density
## [1] 9.175598e-03 0.000000e+00 0.000000e+00 8.244023e-05 1.648805e-04
## [6] 1.483924e-04 1.731245e-04 1.648805e-04 9.068425e-05
## 
## $mids
## [1]  50 150 250 350 450 550 650 750 850
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[8]]
## [[8]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   3   8  18  28  52  50  70  81  81 127 136 249 170  84  45   9   2
## 
## $density
##  [1] 0.0004946414 0.0013190437 0.0029678483 0.0046166529 0.0085737840
##  [6] 0.0082440231 0.0115416323 0.0133553174 0.0133553174 0.0209398186
## [11] 0.0224237428 0.0410552350 0.0280296785 0.0138499588 0.0074196208
## [16] 0.0014839242 0.0003297609
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[2]]
## $breaks
##  [1]  0 10 20 30 40 50 60 70 80 90
## 
## $counts
## [1]  28  96 131 155 149 181 259 199  15
## 
## $density
## [1] 0.002308326 0.007914262 0.010799670 0.012778236 0.012283594 0.014921682
## [7] 0.021352020 0.016405606 0.001236603
## 
## $mids
## [1]  5 15 25 35 45 55 65 75 85
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240
## 
## $counts
##  [1] 270 321 245 158  93  61  37  20   3   1   3   1
## 
## $density
##  [1] 1.112943e-02 1.323166e-02 1.009893e-02 6.512778e-03 3.833471e-03
##  [6] 2.514427e-03 1.525144e-03 8.244023e-04 1.236603e-04 4.122012e-05
## [11] 1.236603e-04 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[4]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 792 275  95  26  13   5   1   5   1
## 
## $density
## [1] 1.305853e-02 4.534213e-03 1.566364e-03 4.286892e-04 2.143446e-04
## [6] 8.244023e-05 1.648805e-05 8.244023e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 793 259  92  41  13  10   4   0   1
## 
## $density
## [1] 1.307502e-02 4.270404e-03 1.516900e-03 6.760099e-04 2.143446e-04
## [6] 1.648805e-04 6.595218e-05 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[6]]
## $breaks
## [1]   0  50 100 150 200 250 300 350 400
## 
## $counts
## [1] 789 262 104  32  11   7   5   3
## 
## $density
## [1] 1.300907e-02 4.319868e-03 1.714757e-03 5.276175e-04 1.813685e-04
## [6] 1.154163e-04 8.244023e-05 4.946414e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 806 242  93  42  14   7   5   3   1
## 
## $density
## [1] 1.328937e-02 3.990107e-03 1.533388e-03 6.924979e-04 2.308326e-04
## [6] 1.154163e-04 8.244023e-05 4.946414e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600
## 
## $counts
##  [1] 813 237  99  32  15   7   7   1   0   0   1   1
## 
## $density
##  [1] 1.340478e-02 3.907667e-03 1.632317e-03 5.276175e-04 2.473207e-04
##  [6] 1.154163e-04 1.154163e-04 1.648805e-05 0.000000e+00 0.000000e+00
## [11] 1.648805e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[9]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280 300
## 
## $counts
##  [1] 277 351 217 148  98  48  28  21   8   6   4   4   2   0   1
## 
## $density
##  [1] 1.141797e-02 1.446826e-02 8.944765e-03 6.100577e-03 4.039571e-03
##  [6] 1.978566e-03 1.154163e-03 8.656224e-04 3.297609e-04 2.473207e-04
## [11] 1.648805e-04 1.648805e-04 8.244023e-05 0.000000e+00 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 838 190 100  40  15  10   7   9   3   0   1
## 
## $density
##  [1] 1.381698e-02 3.132729e-03 1.648805e-03 6.595218e-04 2.473207e-04
##  [6] 1.648805e-04 1.154163e-04 1.483924e-04 4.946414e-05 0.000000e+00
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[8]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000 1100
## 
## $counts
##  [1] 1113    1    3    8   16   21   19   19    9    3    1
## 
## $density
##  [1] 9.175598e-03 8.244023e-06 2.473207e-05 6.595218e-05 1.319044e-04
##  [6] 1.731245e-04 1.566364e-04 1.566364e-04 7.419621e-05 2.473207e-05
## [11] 8.244023e-06
## 
## $mids
##  [1]   50  150  250  350  450  550  650  750  850  950 1050
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[9]]
## [[9]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   5  13  15  19  36  57  54  81 107 144 154 210 184  99  29   4   2
## 
## $density
##  [1] 0.0008244023 0.0021434460 0.0024732069 0.0031327288 0.0059356966
##  [6] 0.0093981863 0.0089035449 0.0133553174 0.0176422094 0.0237427865
## [11] 0.0253915911 0.0346248969 0.0303380049 0.0163231657 0.0047815334
## [16] 0.0006595218 0.0003297609
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[2]]
## $breaks
##  [1]  0 10 20 30 40 50 60 70 80 90
## 
## $counts
## [1]  27 109 128 137 166 181 243 191  31
## 
## $density
## [1] 0.002225886 0.008985985 0.010552350 0.011294312 0.013685078 0.014921682
## [7] 0.020032976 0.015746084 0.002555647
## 
## $mids
## [1]  5 15 25 35 45 55 65 75 85
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220
## 
## $counts
##  [1] 264 336 218 170 107  60  31  13  10   3   1
## 
## $density
##  [1] 1.088211e-02 1.384996e-02 8.985985e-03 7.007420e-03 4.410552e-03
##  [6] 2.473207e-03 1.277824e-03 5.358615e-04 4.122012e-04 1.236603e-04
## [11] 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[4]]
## $breaks
## [1]   0  50 100 150 200 250 300 350 400
## 
## $counts
## [1] 777 280  95  40  15   4   1   1
## 
## $density
## [1] 1.281121e-02 4.616653e-03 1.566364e-03 6.595218e-04 2.473207e-04
## [6] 6.595218e-05 1.648805e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 807 243  91  38  19  11   1   2   1
## 
## $density
## [1] 1.330585e-02 4.006595e-03 1.500412e-03 6.265458e-04 3.132729e-04
## [6] 1.813685e-04 1.648805e-05 3.297609e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 797 261  89  30  15  13   3   1   2   2
## 
## $density
##  [1] 1.314097e-02 4.303380e-03 1.467436e-03 4.946414e-04 2.473207e-04
##  [6] 2.143446e-04 4.946414e-05 1.648805e-05 3.297609e-05 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 798 266  77  34  21   8   7   0   2
## 
## $density
## [1] 1.315746e-02 4.385820e-03 1.269580e-03 5.605936e-04 3.462490e-04
## [6] 1.319044e-04 1.154163e-04 0.000000e+00 3.297609e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 803 260  83  36  17   4   4   2   1   1   2
## 
## $density
##  [1] 1.323990e-02 4.286892e-03 1.368508e-03 5.935697e-04 2.802968e-04
##  [6] 6.595218e-05 6.595218e-05 3.297609e-05 1.648805e-05 1.648805e-05
## [11] 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[9]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280 300 320
## 
## $counts
##  [1] 293 343 240 119  83  58  29  22   9   6   6   0   1   2   1   1
## 
## $density
##  [1] 1.207749e-02 1.413850e-02 9.892828e-03 4.905194e-03 3.421270e-03
##  [6] 2.390767e-03 1.195383e-03 9.068425e-04 3.709810e-04 2.473207e-04
## [11] 2.473207e-04 0.000000e+00 4.122012e-05 8.244023e-05 4.122012e-05
## [16] 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290 310
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600
## 
## $counts
##  [1] 837 197  93  36  22   7   7   5   2   4   2   1
## 
## $density
##  [1] 1.380049e-02 3.248145e-03 1.533388e-03 5.935697e-04 3.627370e-04
##  [6] 1.154163e-04 1.154163e-04 8.244023e-05 3.297609e-05 6.595218e-05
## [11] 3.297609e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[9]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1113    0    0   10   17   22   21   18   11    1
## 
## $density
##  [1] 9.175598e-03 0.000000e+00 0.000000e+00 8.244023e-05 1.401484e-04
##  [6] 1.813685e-04 1.731245e-04 1.483924e-04 9.068425e-05 8.244023e-06
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[10]]
## [[10]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
## 
## $counts
##  [1]   4   9  21  29  26  40  62  80  86 136 212 243 166  69  25   4   1
## 
## $density
##  [1] 0.0006595218 0.0014839242 0.0034624897 0.0047815334 0.0042868920
##  [6] 0.0065952185 0.0102225886 0.0131904369 0.0141797197 0.0224237428
## [11] 0.0349546579 0.0400659522 0.0273701566 0.0113767519 0.0041220115
## [16] 0.0006595218 0.0001648805
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5 82.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
## 
## $counts
##  [1]  31  99 136 141 162 183 222 207  31   1
## 
## $density
##  [1] 2.555647e-03 8.161583e-03 1.121187e-02 1.162407e-02 1.335532e-02
##  [6] 1.508656e-02 1.830173e-02 1.706513e-02 2.555647e-03 8.244023e-05
## 
## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220
## 
## $counts
##  [1] 271 318 244 151 107  52  37  21   4   7   1
## 
## $density
##  [1] 1.117065e-02 1.310800e-02 1.005771e-02 6.224237e-03 4.410552e-03
##  [6] 2.143446e-03 1.525144e-03 8.656224e-04 1.648805e-04 2.885408e-04
## [11] 4.122012e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[4]]
## $breaks
## [1]   0  50 100 150 200 250 300 350
## 
## $counts
## [1] 789 270 100  30  10   7   7
## 
## $density
## [1] 0.0130090684 0.0044517725 0.0016488046 0.0004946414 0.0001648805
## [6] 0.0001154163 0.0001154163
## 
## $mids
## [1]  25  75 125 175 225 275 325
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 802 253  92  31  19   5   8   1   0   2
## 
## $density
##  [1] 1.322341e-02 4.171476e-03 1.516900e-03 5.111294e-04 3.132729e-04
##  [6] 8.244023e-05 1.319044e-04 1.648805e-05 0.000000e+00 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 798 262  79  39  18   7   5   1   2   1   0   0   1
## 
## $density
##  [1] 1.315746e-02 4.319868e-03 1.302556e-03 6.430338e-04 2.967848e-04
##  [6] 1.154163e-04 8.244023e-05 1.648805e-05 3.297609e-05 1.648805e-05
## [11] 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 823 232  82  37  17  11   5   1   3   1   1
## 
## $density
##  [1] 1.356966e-02 3.825227e-03 1.352020e-03 6.100577e-04 2.802968e-04
##  [6] 1.813685e-04 8.244023e-05 1.648805e-05 4.946414e-05 1.648805e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 825 213 104  38  17   8   1   2   2   1   1   0   1
## 
## $density
##  [1] 1.360264e-02 3.511954e-03 1.714757e-03 6.265458e-04 2.802968e-04
##  [6] 1.319044e-04 1.648805e-05 3.297609e-05 3.297609e-05 1.648805e-05
## [11] 1.648805e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[9]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240
## 
## $counts
##  [1] 290 337 228 146  81  55  28  19  13   9   3   4
## 
## $density
##  [1] 0.0119538335 0.0138911789 0.0093981863 0.0060181369 0.0033388293
##  [6] 0.0022671063 0.0011541632 0.0007831822 0.0005358615 0.0003709810
## [11] 0.0001236603 0.0001648805
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 831 208  81  39  26  12   6   5   2   2   1
## 
## $density
##  [1] 1.370157e-02 3.429514e-03 1.335532e-03 6.430338e-04 4.286892e-04
##  [6] 1.978566e-04 9.892828e-05 8.244023e-05 3.297609e-05 3.297609e-05
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[10]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1113    0    2    6   21   21   20   19    8    3
## 
## $density
##  [1] 9.175598e-03 0.000000e+00 1.648805e-05 4.946414e-05 1.731245e-04
##  [6] 1.731245e-04 1.648805e-04 1.566364e-04 6.595218e-05 2.473207e-05
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[11]]
## [[11]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
## 
## $counts
##  [1]   4   5  19  23  42  52  54  71  81 135 206 262 164  64  27   4
## 
## $density
##  [1] 0.0006595218 0.0008244023 0.0031327288 0.0037922506 0.0069249794
##  [6] 0.0085737840 0.0089035449 0.0117065128 0.0133553174 0.0222588623
## [11] 0.0339653751 0.0431986810 0.0270403957 0.0105523495 0.0044517725
## [16] 0.0006595218
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100
## 
## $counts
##  [1]  37  73 145 183 146 179 206 191  51   2
## 
## $density
##  [1] 0.0030502885 0.0060181369 0.0119538335 0.0150865622 0.0120362737
##  [6] 0.0147568013 0.0169826876 0.0157460841 0.0042044518 0.0001648805
## 
## $mids
##  [1]  5 15 25 35 45 55 65 75 85 95
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200
## 
## $counts
##  [1] 240 334 254 164 106  57  29  23   4   2
## 
## $density
##  [1] 9.892828e-03 1.376752e-02 1.046991e-02 6.760099e-03 4.369332e-03
##  [6] 2.349547e-03 1.195383e-03 9.480627e-04 1.648805e-04 8.244023e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[4]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260 280 300 320
## 
## $counts
##  [1] 367 309 189 100  92  56  36  21  12   8  12   4   3   2   0   2
## 
## $density
##  [1] 1.512778e-02 1.273702e-02 7.790602e-03 4.122012e-03 3.792251e-03
##  [6] 2.308326e-03 1.483924e-03 8.656224e-04 4.946414e-04 3.297609e-04
## [11] 4.946414e-04 1.648805e-04 1.236603e-04 8.244023e-05 0.000000e+00
## [16] 8.244023e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250 270 290 310
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[5]]
## $breaks
## [1]   0  50 100 150 200 250 300 350
## 
## $counts
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## $density
## [1] 1.314097e-02 4.369332e-03 1.335532e-03 6.595218e-04 2.802968e-04
## [6] 1.154163e-04 9.892828e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 802 249  85  51  14   7   4   0   0   0   1
## 
## $density
##  [1] 1.322341e-02 4.105523e-03 1.401484e-03 8.408904e-04 2.308326e-04
##  [6] 1.154163e-04 6.595218e-05 0.000000e+00 0.000000e+00 0.000000e+00
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 811 235  92  43  20   9   0   2   1
## 
## $density
## [1] 1.337181e-02 3.874691e-03 1.516900e-03 7.089860e-04 3.297609e-04
## [6] 1.483924e-04 0.000000e+00 3.297609e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 796 258  81  49  12   9   5   1   1   1
## 
## $density
##  [1] 1.312448e-02 4.253916e-03 1.335532e-03 8.079143e-04 1.978566e-04
##  [6] 1.483924e-04 8.244023e-05 1.648805e-05 1.648805e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[9]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200 220 240 260
## 
## $counts
##  [1] 270 357 227 162  71  52  27  17  12   9   1   4   4
## 
## $density
##  [1] 1.112943e-02 1.471558e-02 9.356966e-03 6.677659e-03 2.926628e-03
##  [6] 2.143446e-03 1.112943e-03 7.007420e-04 4.946414e-04 3.709810e-04
## [11] 4.122012e-05 1.648805e-04 1.648805e-04
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190 210 230 250
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600
## 
## $counts
##  [1] 847 197  78  37  25   7   8   5   5   1   1   2
## 
## $density
##  [1] 1.396538e-02 3.248145e-03 1.286068e-03 6.100577e-04 4.122012e-04
##  [6] 1.154163e-04 1.319044e-04 8.244023e-05 8.244023e-05 1.648805e-05
## [11] 1.648805e-05 3.297609e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[11]][[11]]
## $breaks
##  [1]    0  100  200  300  400  500  600  700  800  900 1000
## 
## $counts
##  [1] 1113    0    1   10   13   25   22   17   11    1
## 
## $density
##  [1] 9.175598e-03 0.000000e+00 8.244023e-06 8.244023e-05 1.071723e-04
##  [6] 2.061006e-04 1.813685e-04 1.401484e-04 9.068425e-05 8.244023e-06
## 
## $mids
##  [1]  50 150 250 350 450 550 650 750 850 950
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## 
## [[12]]
## [[12]][[1]]
## $breaks
##  [1]  0  5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
## 
## $counts
##  [1]   7   6  21  20  30  31  55  57  85 154 280 262 130  61  13   1
## 
## $density
##  [1] 0.0011541632 0.0009892828 0.0034624897 0.0032976092 0.0049464138
##  [6] 0.0051112943 0.0090684254 0.0093981863 0.0140148392 0.0253915911
## [11] 0.0461665293 0.0431986810 0.0214344600 0.0100577082 0.0021434460
## [16] 0.0001648805
## 
## $mids
##  [1]  2.5  7.5 12.5 17.5 22.5 27.5 32.5 37.5 42.5 47.5 52.5 57.5 62.5 67.5 72.5
## [16] 77.5
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[2]]
## $breaks
##  [1]   0  10  20  30  40  50  60  70  80  90 100 110
## 
## $counts
##  [1]  41  74 144 189 166 168 166 161  86  17   1
## 
## $density
##  [1] 3.380049e-03 6.100577e-03 1.187139e-02 1.558120e-02 1.368508e-02
##  [6] 1.384996e-02 1.368508e-02 1.327288e-02 7.089860e-03 1.401484e-03
## [11] 8.244023e-05
## 
## $mids
##  [1]   5  15  25  35  45  55  65  75  85  95 105
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[3]]
## $breaks
##  [1]   0  20  40  60  80 100 120 140 160 180 200
## 
## $counts
##  [1] 267 325 242 144 117  63  26  14  13   2
## 
## $density
##  [1] 1.100577e-02 1.339654e-02 9.975268e-03 5.935697e-03 4.822754e-03
##  [6] 2.596867e-03 1.071723e-03 5.770816e-04 5.358615e-04 8.244023e-05
## 
## $mids
##  [1]  10  30  50  70  90 110 130 150 170 190
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[4]]
## $breaks
## [1]   0  50 100 150 200 250 300 350 400
## 
## $counts
## [1] 782 291  81  35  10   7   6   1
## 
## $density
## [1] 1.289365e-02 4.798021e-03 1.335532e-03 5.770816e-04 1.648805e-04
## [6] 1.154163e-04 9.892828e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[5]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 804 255  92  34  12   8   3   4   1
## 
## $density
## [1] 1.325639e-02 4.204452e-03 1.516900e-03 5.605936e-04 1.978566e-04
## [6] 1.319044e-04 4.946414e-05 6.595218e-05 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[6]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 806 242 100  36  13   9   2   3   1   1
## 
## $density
##  [1] 1.328937e-02 3.990107e-03 1.648805e-03 5.935697e-04 2.143446e-04
##  [6] 1.483924e-04 3.297609e-05 4.946414e-05 1.648805e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[7]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500
## 
## $counts
##  [1] 808 247  87  36  13  13   5   2   1   1
## 
## $density
##  [1] 1.332234e-02 4.072547e-03 1.434460e-03 5.935697e-04 2.143446e-04
##  [6] 2.143446e-04 8.244023e-05 3.297609e-05 1.648805e-05 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[8]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550
## 
## $counts
##  [1] 810 231  98  44  17   7   3   1   1   0   1
## 
## $density
##  [1] 1.335532e-02 3.808739e-03 1.615829e-03 7.254740e-04 2.802968e-04
##  [6] 1.154163e-04 4.946414e-05 1.648805e-05 1.648805e-05 0.000000e+00
## [11] 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[9]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450
## 
## $counts
## [1] 734 364  84  23   6   1   0   0   1
## 
## $density
## [1] 1.210223e-02 6.001649e-03 1.384996e-03 3.792251e-04 9.892828e-05
## [6] 1.648805e-05 0.000000e+00 0.000000e+00 1.648805e-05
## 
## $mids
## [1]  25  75 125 175 225 275 325 375 425
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[10]]
## $breaks
##  [1]   0  50 100 150 200 250 300 350 400 450 500 550 600 650
## 
## $counts
##  [1] 826 218  80  45  18   7   6   5   4   1   2   0   1
## 
## $density
##  [1] 1.361913e-02 3.594394e-03 1.319044e-03 7.419621e-04 2.967848e-04
##  [6] 1.154163e-04 9.892828e-05 8.244023e-05 6.595218e-05 1.648805e-05
## [11] 3.297609e-05 0.000000e+00 1.648805e-05
## 
## $mids
##  [1]  25  75 125 175 225 275 325 375 425 475 525 575 625
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
## 
## [[12]][[11]]
## $breaks
##  [1]   0 100 200 300 400 500 600 700 800 900
## 
## $counts
## [1] 1113    0    0    5   15   27   28   19    6
## 
## $density
## [1] 9.175598e-03 0.000000e+00 0.000000e+00 4.122012e-05 1.236603e-04
## [6] 2.225886e-04 2.308326e-04 1.566364e-04 4.946414e-05
## 
## $mids
## [1]  50 150 250 350 450 550 650 750 850
## 
## $xname
## [1] "X[[i]]"
## 
## $equidist
## [1] TRUE
## 
## attr(,"class")
## [1] "histogram"
Skewness <- data.frame("Skewness"=as.vector(pbsapply(scores, function(x) sapply(x, skewness))),
                       "Dropout"=rep(dropout_percent, each=length(dim_val)),
                       "Dimension"=dim_val)
ggplot(Skewness, aes(x=Dimension, y=Skewness)) +
  geom_line(aes(group=Dropout)) +
  geom_point(aes(color=Dropout))

Antihub <- data.frame("Antihub"=as.vector(pbsapply(scores, function(x) sapply(x, antihub))),
                      "Dropout"=rep(dropout_percent, each=length(dim_val)),
                      "Dimension"=dim_val)
ggplot(Antihub, aes(x=Dimension, y=Antihub)) +
  geom_line(aes(group=Dropout)) +
  geom_point(aes(color=Dropout))

KThd <- data.frame("KThd"=as.vector(pbsapply(scores, function(x) sapply(x, function(y) k_thd(y,k)))),
                   "Dropout"=rep(dropout_percent, each=length(dim_val)),
                   "Dimension"=dim_val)
ggplot(KThd, aes(x=Dimension, y=KThd)) +
  geom_line(aes(group=Dropout)) +
  geom_point(aes(color=Dropout))

MeanSdThd <- data.frame("MeanSdThd"=as.vector(pbsapply(scores, function(x) sapply(x, meansd_thd))),
                        "Dropout"=rep(dropout_percent, each=length(dim_val)),
                        "Dimension"=dim_val)
ggplot(MeanSdThd, aes(x=Dimension, y=MeanSdThd)) +
  geom_line(aes(group=Dropout)) +
  geom_point(aes(color=Dropout))

Asymmetry <- data.frame("Asymmetry"=as.vector(pbsapply(scores, function(x) sapply(x, asymmetry_evaluation))),
                        "Dropout"=rep(dropout_percent, each=length(dim_val)),
                        "Dimension"=dim_val)
ggplot(Asymmetry, aes(x=Dimension, y=Asymmetry)) +
  geom_line(aes(group=Dropout)) +
  geom_point(aes(color=Dropout))

rc <- pbsapply(simul_pca, function(x) sapply(dim_val, function(y) relative_contrast(x[1:y,])))
link_df <- data.frame("Relative_contrast"=as.vector(rc),
                      "Asymmetry"=Asymmetry$Asymmetry,
                      "Skewness"=Skewness$Skewness,
                      "Dimension"=dim_val,
                      "Dropout"=rep(dropout_percent, each=length(dim_val)))

lm <- lm(Skewness ~ log(Relative_contrast), data=link_df)
summary(lm)
## 
## Call:
## lm(formula = Skewness ~ log(Relative_contrast), data = link_df)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.40781 -0.64339 -0.00547  0.52833  2.69159 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)             2.06937    0.07535   27.46   <2e-16 ***
## log(Relative_contrast) -0.43186    0.02712  -15.92   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8657 on 130 degrees of freedom
## Multiple R-squared:  0.661,  Adjusted R-squared:  0.6584 
## F-statistic: 253.5 on 1 and 130 DF,  p-value: < 2.2e-16
ggplot(link_df, aes(x=log(Relative_contrast), y=Skewness, color=Dropout)) +
  geom_point() +
  geom_abline(slope = lm$coefficients[2], intercept = lm$coefficients[1], color="red")

# Do pearson and spearman also
lm <- lm(Asymmetry ~ log(Relative_contrast), data=link_df)
summary(lm)
## 
## Call:
## lm(formula = Asymmetry ~ log(Relative_contrast), data = link_df)
## 
## Residuals:
##        Min         1Q     Median         3Q        Max 
## -1.143e-15 -3.833e-16 -1.784e-16  3.770e-17  2.434e-14 
## 
## Coefficients:
##                         Estimate Std. Error   t value Pr(>|t|)    
## (Intercept)            1.000e+00  1.902e-16 5.256e+15   <2e-16 ***
## log(Relative_contrast) 1.562e-16  6.848e-17 2.281e+00   0.0242 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.186e-15 on 130 degrees of freedom
## Multiple R-squared:  0.4998, Adjusted R-squared:  0.496 
## F-statistic: 129.9 on 1 and 130 DF,  p-value: < 2.2e-16
ggplot(link_df, aes(x=log(Relative_contrast), y=Asymmetry, color=Dropout)) +
  geom_point() +
  geom_abline(slope = lm$coefficients[2], intercept = lm$coefficients[1], color="red")